AUTHOR: Mara D. Neusel TITLE: The Lasker-Noether Theorem in the Category $U(\H^*)$ (denizin kokusu) Journal of Pure and Applied Algebra -- to appear -- We prove the Lasker-Noether Theorem in the category $U(\H^*)$ of unstable $\H^*\odot \P^*$-modules. Along the way, we generalize Lam's $\J$-functor to the context of modules. AMS CODE: 55S10 Steenrod Algebra, 13A50 Invariant Theory, 13XX Commutative Rings and Algebras, 55XX Algebraic Topology KEY WORDS: Lasker-Noether Theorem, Unstable Modules, Steenrod Algebra, Dickson Algebra, Polynomial Invariants of Finite Groups